California Tours is planning a group bus trip that for the following candidate c

Question

California Tours is planning a group bus trip that for the following candidate cities in the table below. Also included are the total costs for the group to visit those cities on the tour. To plan the trip, three prioritized goals are listed below, in order of importance. P1: Avoid spending more than $15000 for the total trip. P2: Visit at least 5 cities. P3: Include San Mateo in the tour. a. Formulate a goal programming model that will help to determine the number of cities to include in the tour. b. Find the optimal solution using Solver. (Provide a printout of the Answer report and the Excel spreadsheet formulation). c. Include a managerial statement that describes verbally the results.

Explanation / Answer

Let Xi = 1

if bus stops at city i0 otherwisewhere i= 1(SF), 2(OK), 3(PA), …, 8(MN)

dj-: underachievement of goal j

dj+: overachievement of goal j

where j = 1, 2, 3(note that d3+ is not possible since X5 is binary)

Min P1(d1+) + P2(d2-) + P3[(d3-)+(d3+)] or

Min P1(d1+) + P2(d2-) + P3(d3-) OR

Min P1(d1+), P2(d2-), P3[(d3-)+(d3+)] or

Min P1(d1+), P2(d2-), P3(d3-)

Subject to$5000X1+4500X2+…+8000X8 + (d1-) – (d1+) = 15,000

X1+X2+X3+X4+X5+X6+X7+X8 + (d2-) – (d2+) = 5

X5 + (d3-) = 1 ORX5 + (d3-) – (d3+) = 1 (because X5 is a binary variable then both correct)

Xi = 0 or 1 for all i= 1, 2, …,

8di-, di+ >= 0

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